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2 years ago

Rewrite 2x2x2 using an exponent.

Mathematics

1 answer:

Nastasia [14]2 years ago

6 0

Answer:

2³

Step-by-step explanation:

please mark me as brainliest

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The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha

Xelga [282]

Answer:

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

Step-by-step explanation:

Let suppose that function $f$ is continuous and integrable in the given intervals, by integral definition of average we have that:

$\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6$ (1)

$\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20$ (2)

By Fundamental Theorems of Calculus we expand both expressions:

$\frac{F(3)-F(-2)}{3-(-2)} = -6$

$F(3) - F(-2) = -30$ (1b)

$\frac{F(5)-F(3)}{5-3} = 20$

$F(5) - F(3) = 40$ (2b)

We obtain the average value of $f$ over the interval $[-2, 5]$ by algebraic handling:

$F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)$

$F(5) - F(-2) = 10$

$\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}$

$\bar f = \frac{10}{7}$

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

4 0

2 years ago

Match each set of numbers with their least common multiple.

mylen [45]

Answer:

27, 12, and 36 = 108

22 and 4 = 44

14 and 12 = 84

25 and 8 =200

9, 8, and 7 = 504

32, 24, and 18 = 288

Step-by-step explanation: You are welcome.

5 0

2 years ago

Out of 230 students, 11% chose gymnastics as their favorite sport. How many students does 11% represent? *

joja [24]

Answer:

Step-by-step explanation:

$11\% \: of \: 230 \\ \\ = \frac{11}{100} \times 230 \\ \\ = 0.11 \times 230 \\ \\ = 25.3 \\ = 25$

Hence 11% represents 25 students.

5 0

2 years ago

Solve the equation -2(m-30)=-6m

Sergio039 [100]

Answer:

m=-15

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. m=-15

7 0

2 years ago

The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the sam

Amiraneli [1.4K]

Answer:

The equation is:

$j/g=5/2$

Or, what is equivalent:

$j=5g/2$

Explanation:

This is the table that shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe:

Lemon juice (mL) Sugar (g)

Batch A 500 200

Batch B 750 300

Batch C 1500 600

You need to write an equation to describe the relationship between j, the amount of lemon juice in mL and s, the amount of sugar in g.

Calculate some ratios, to determine the kind of relation between the amount of juice and the amount of sugar in the recipe.

Batch A: lemon juice / sugar = 500 / 200 = 5/2

Batch B: lemon juice / sugar = 750/300 = 5/2

Batch C: lemon juice / sugar = 1500/600 = 5/2

Hence, the amount of juice, j, and the amound of sugar, s, are proportional and the constant of proportionality is 5/2. From this, the equation is:

$j/g=5/2$

Or, what is equivalent (solving for j):

$j=5g/2$

3 0

2 years ago